Sounds like you got a good deal on the buckets/carboys, etc., but the recipe is a bit "too" basic in my opinion. It's probably a decent recipe for the ultra-beginner, but I don't believe the end result will meet your expectations (especially using corn syrup).
I checked online & found a
few homebrew stores in Modesto
(nothing in Stockton, sadly...), and I'd suggest heading to one of those spots & talk with them about decent starter recipes as well as what other equipment you need.
Equipment-wise, you'll also need:
-Bungs & airlocks if the carboys didn't come with them
-A kettle (think I started with a basic 10-gallon)
-Sanitizer (iodine based or Star-San if you want my recommendation)
-Stirring spoon (decent size, about 1.5' to 2' long is the average)
-Thermometer, preferably digital (glass ones tend to break easily if you're not careful with them)
-A way of cooling the wort, either a copper chiller or just set the kettle in a tub full of cold water & swap out frozen water bottles-there's a lot of threads here on how to do that
-Would also highly
recommend a Wine Thief & auto siphon. You'll thank me later.
-Tubing for transferring to/from your fermenter (size depends on the type of siphon you get)
-A large Rubbermaid tub (so you can hold a large amount of sanitizer in one spot--good for spot cleaning or sanitizing a huge amount of bottles)
-A bottling wand (must get)
-A copy of Charlie Papazian's "The Complete Joy of Homebrewing", or head to HowToBrew
by John Palmer & research, research, research.
Since you love IPA's like I do, I'd suggest asking the homebrew shop if they have a recipe book (many reputable spots have their own homespun recipe books) & see if they have a basic extract IPA recipe you can try out.
It's an investment, but well worth it when you get the basics figured out. Good luck & welcome to the addiction!